Authors : Shamshuritawati Sharif, Nuraimi Ruslan and Tareq A.M. Atiany
Abstract: Classical Box M-statisticis one of Likelihood Ratio Test (LRT) constructed under the multivariate normality distribution. The performance of classical Box M-statistic by using classical estimators suffers from masking and swamping effects when the outlier occurs in data set. To alleviate the problem, robust estimators are recommended. In this study, a robust Box M-statistic based on a S-estimator, Ms and M-estimator MM are proposed as the alternative to the classical Box M-statistic. Over the simulation study, the performance comparisonof classical, Ms and MM-statistics are measured using type 1 error rates. From the results, it showed that Ms (Box M-statistic based on S-estimator) has a competitive performance relative to MM and the classicalstatistic. In summary, Ms can be used for testing the equality of two difference covariance matrices or more when the data contains outlier.
Shamshuritawati Sharif, Nuraimi Ruslan and Tareq A.M. Atiany, 2018. Type 1 Error Rate Comparison Between Classical and Modified Box M-Statistic. Journal of Engineering and Applied Sciences, 13: 1246-1252.